(x-4)(x-4)-(4x+5)(3x-10)=17x-110quad5? eching

$$( x - 4 ) ( x - 4 ) - ( 4 x + 5 ) ( 3 x - 10 ) = 17 x - 110 \quad 5 ?$$

x uchun yechish

$$x=2\sqrt{14}\approx 7,483314774$$

$$x=-2\sqrt{14}\approx -7,483314774$$

Kvadrat ildizini topish bo'yicha qadamlar

\left(x-4\right)^{2} hosil qilish uchun x-4 va x-4 ni ko'paytirish.

$$\left(x-4\right)^{2}-\left(4x+5\right)\left(3x-10\right)=17x-110\times 5$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-4\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-8x+16-\left(4x+5\right)\left(3x-10\right)=17x-110\times 5$$

4x+5 ga 3x-10 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-8x+16-\left(12x^{2}-25x-50\right)=17x-110\times 5$$

12x^{2}-25x-50 teskarisini topish uchun har birining teskarisini toping.

$$x^{2}-8x+16-12x^{2}+25x+50=17x-110\times 5$$

-11x^{2} ni olish uchun x^{2} va -12x^{2} ni birlashtirish.

$$-11x^{2}-8x+16+25x+50=17x-110\times 5$$

17x ni olish uchun -8x va 25x ni birlashtirish.

$$-11x^{2}+17x+16+50=17x-110\times 5$$

66 olish uchun 16 va 50'ni qo'shing.

$$-11x^{2}+17x+66=17x-110\times 5$$

550 hosil qilish uchun 110 va 5 ni ko'paytirish.

$$-11x^{2}+17x+66=17x-550$$

Ikkala tarafdan 17x ni ayirish.

$$-11x^{2}+17x+66-17x=-550$$

0 ni olish uchun 17x va -17x ni birlashtirish.

$$-11x^{2}+66=-550$$

Ikkala tarafdan 66 ni ayirish.

$$-11x^{2}=-550-66$$

-616 olish uchun -550 dan 66 ni ayirish.

$$-11x^{2}=-616$$

Ikki tarafini -11 ga bo‘ling.

$$x^{2}=\frac{-616}{-11}$$

56 ni olish uchun -616 ni -11 ga bo‘ling.

$$x^{2}=56$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2\sqrt{14} x=-2\sqrt{14}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(x-4\right)^{2} hosil qilish uchun x-4 va x-4 ni ko'paytirish.

$$\left(x-4\right)^{2}-\left(4x+5\right)\left(3x-10\right)=17x-110\times 5$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-4\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-8x+16-\left(4x+5\right)\left(3x-10\right)=17x-110\times 5$$

4x+5 ga 3x-10 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-8x+16-\left(12x^{2}-25x-50\right)=17x-110\times 5$$

12x^{2}-25x-50 teskarisini topish uchun har birining teskarisini toping.

$$x^{2}-8x+16-12x^{2}+25x+50=17x-110\times 5$$

-11x^{2} ni olish uchun x^{2} va -12x^{2} ni birlashtirish.

$$-11x^{2}-8x+16+25x+50=17x-110\times 5$$

17x ni olish uchun -8x va 25x ni birlashtirish.

$$-11x^{2}+17x+16+50=17x-110\times 5$$

66 olish uchun 16 va 50'ni qo'shing.

$$-11x^{2}+17x+66=17x-110\times 5$$

550 hosil qilish uchun 110 va 5 ni ko'paytirish.

$$-11x^{2}+17x+66=17x-550$$

Ikkala tarafdan 17x ni ayirish.

$$-11x^{2}+17x+66-17x=-550$$

0 ni olish uchun 17x va -17x ni birlashtirish.

$$-11x^{2}+66=-550$$

550 ni ikki tarafga qo’shing.

$$-11x^{2}+66+550=0$$

616 olish uchun 66 va 550'ni qo'shing.

$$-11x^{2}+616=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -11 ni a, 0 ni b va 616 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-11\right)\times 616}}{2\left(-11\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-11\right)\times 616}}{2\left(-11\right)}$$

-4 ni -11 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{44\times 616}}{2\left(-11\right)}$$

44 ni 616 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{27104}}{2\left(-11\right)}$$

27104 ning kvadrat ildizini chiqarish.

$$x=\frac{0±44\sqrt{14}}{2\left(-11\right)}$$

2 ni -11 marotabaga ko'paytirish.

$$x=\frac{0±44\sqrt{14}}{-22}$$

x=\frac{0±44\sqrt{14}}{-22} tenglamasini yeching, bunda ± musbat.

$$x=-2\sqrt{14}$$

x=\frac{0±44\sqrt{14}}{-22} tenglamasini yeching, bunda ± manfiy.

$$x=2\sqrt{14}$$

Tenglama yechildi.

$$x=-2\sqrt{14} x=2\sqrt{14}$$